Symmetry If a function does not change when any possible pair of variables are exchanged it is said to be totally symmetric
{"Image DocumentName": "Symmetry If a function does not change when any possible pair of variables are exchanged it is said to be totally symmetric", "Image ImageDescription": "2n+1 symmetric functions of n variables. If a function does not change when any possible pair of a SUBSET of variables are exchanged, it is said to be partially symmetric Symmetric functions can be synthesized with fewer logic elements. Detection of symmetry is an important and HARD problem in CAD. There are several other types of symmetry \u2013 we will examine these in more detail later in class. EXAMPLES of totally symmetric and partially symmetric functions. f(x,y,z) = x\uf0a2y \uf0a2z + xy \uf0a2z \uf0a2 + x \uf0a2yz \uf0a2 - Totally Symmetric. f(x,y,z) = x \uf0a2y \uf0a2z + x \uf0a2yz \uf0a2 + xyz - Partially Symmetric (y,z)", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}